Japan's All Nippon Airways has more 787s in its fleet -- 17 as of Dec. 31 -- as the launch customer of the Dreamliner. An ANA spokeswoman told Bloomberg News the airline isn't doing anything different with its fleet in light of the fire. However, the carrier received instruction from Japan's transport ministry to check all 787s and inspect the jet's batteries.

According to FlightAware, several 787s are in the air, many on long-haul flights.

"The FAA is not likely to take any immediate action," Leake said. "But the 787 has run out of mulligans, and even though this may be an unrelated battery issue, any new electrical event could have the FAA take more drastic measures to include the grounding of the fleet."

Jefferies analyst Howard A. Rubel tends to disagree, telling the Associated Press that the drop in Boeing's shares may be overdone.

Rubel wrote that the decline of over $1 billion in market value "would seem to overstate the worry.”

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